To calculate the account balance after 4 years with compound interest, we can use the compound interest formula:

$A = P \left( 1 + \frac{r}{n} \right)^{nt}$

Where:

• $A$ is the account balance after time $t$.
• $P$ is the principal (initial deposit), which is $2,000.
• $r$ is the annual interest rate (decimal form), so 3.4% = 0.034.
• $n$ is the number of times the interest is compounded per year. Since it's compounded quarterly, $n = 4$.
• $t$ is the number of years the money is invested, which is 4 years.

Substituting the given values:

$A = 2000 \left( 1 + \frac{0.034}{4} \right)^{4 \times 4}$

Now, let's calculate it step by step:

1. First, calculate $\frac{0.034}{4} = 0.0085$.
2. Then, $1 + 0.0085 = 1.0085$.
3. Next, calculate $4 \times 4 = 16$.
4. Now, raise $1.0085$ to the power of 16:
   $1.0085^{16} \approx 1.148574$
5. Finally, multiply the result by the principal amount:
   $2000 \times 1.148574 \approx 2297.15$

Thus, the account balance after 4 years is 2297.15 (rounded to the nearest cent).

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Would you like further explanation on how to use this formula or how compound interest works in general? Here are some related questions you might find interesting:

1. How do different compounding frequencies affect the final account balance?
2. What would happen if the interest rate were higher, say 5%?
3. How would the balance change if Ashley had deposited a larger or smaller amount?
4. What is the difference between compound interest and simple interest?
5. How can you calculate compound interest using a financial calculator?

Tip: To maximize the growth of your savings, consider making regular contributions to the account in addition to your initial deposit.